I have a 805 axis that I've carried for two years. I have abused it no end, and it is still OK. I usually carry one AFCK style knife and two smaller knives, those are usually spydercos.
The 806 AFCK is the old AFCK with the liner lock replaced by the axis lock. The AFCK was a Chris Carraci tactical design based on the old Spyderco police model(That's what Chris says). I think he was the first one to put the cutout for your finger in the handle. I'm not sure about the fingershelf to choke up on the handle, that's been around for sometime. I like the fingershelf, it allows me much more control when using the blade. Your longest finger in the cutout will prevent your index finger slipping off the fingershelf onto the blade.
Sadly, Chris no longer works with either Spyderco or BM. There were some issues, I believe. Chris was also critical of the new axis AFCK.
Also, in the beginning, I think Spyderco didn't want to do the AFCK as it was concerned with PC, and the fear that folders specifically meant for cutting people would result in all folders being banned. So Chris went to BM.
Going back to the knife:
The cutout is supposed to guide your hand into a good grip on the handle fast, a "tactical" quality. Also, when pulling back on the drawcut, you pull on the cutout with your index finger to retain the handle.
The curved back of the handle allows a palm-reinforced grip, that helps your hand not slip onto blade on heavy impacts or thrusts(if the handle is slippery with blood, etc). You mat notice that the G-10 of the BM handle is smoother than many other brands. I like it that way, because it slides in an out of the pocket more easily. The problem is that it gets slippery more easily, hence the usefulness of the cutout and the rounded butt.
It appears that the martial arts community embraced the AFCK. Its variants with roughly the same kind of handle are the Emerson Commander(with the wave opener), Spyderco Yojimbo and a whole lot of other models from other brands. You could say that maybe tactical knives are supposed to have the same characteristics as the AFCK.
The old linerlock AFCK had the clip placed on the pivot end, to ride tip down. To me, this is the way the AFCK works best, if you are concerned about ease and speed of presentation.
But when BM put the axis lock on it, it was given the option of having the clip on the butt end, to ride tip-up. In my opinion, this is not ideal, for the 806, with its oval hole. It needs much more to upend the knife, shuffle your grip up(since the handle is long) and stick your thumb into the hole, you could miss it under stress.
With the stud, it is a bit easier, so that's my choice, since the 440C is OK for me.
If you carry firearms then this is not relevant, as your AFCK might be more of a utility knife.
Also the 805 has a higher grind, might be better in slicing?
Lastly, when carried tip-up, the AFCK has a very low profile, if you are carrying it in your vertical slacks pocket instead of jeans. No metal shows, just a little bit of butt and the clip. The way it clips, it also does not cause funny ripples around your pocket. Not many folders carry this way.
To me, the AFCK is a very "safe" knife. It does everything OK.